Unmanned aerial vehicles (UAVs) can be used for a wide variety of applications, including agriculture, infrastructure maintenance, and disaster response. In this paper, we focus on the use of UAVs for disaster response. Multiple UAVs equipped with communication terminals can be deployed to construct an airborne network connecting isolated areas. Another use is for real-time video transmission from a UAV to a ground station, using multiple UAVs operating simultaneously by different organizations, e.g., rescue teams, fire departments, broadcasting companies, and so forth. In both cases, frequency resources must be shared efficiently among adjacent UAVs. Thus, we describe a radio resource management system for UAVs. The focus of this paper is data communications, rather than the broader issue of command and control communications. First, we present experimental results from field experiments using WiFi communication terminals that do not have centralized radio resource management functionality. Then, we propose a centralized resource allocation technique that assumes an orthogonal frequency division multiplexing (OFDM)-based communication system, using resource blocks consistent with the long-term evolution (LTE) standard.